Questions on the circle, a curve composed of points that are at a fixed distance from a fixed point.

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3
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2answers
269 views

Circle bitangent angles

Say we have two circles $C_1$ and $C_2$ with radii $r_1$ and $r_2$, respectively. Let their centers be $d$ units apart. There are 4 bitangents, two outer and two inner. Examine the intersection of an ...
2
votes
4answers
3k views

line segment joining two centers of circles is perpendicular to line segment joining two intersection point of the circles

Prove that the line segment joining the two centers of the concurrent circles of equal radius is perpendicular to line segment joining the two intersection points of the circles. I had come across ...
3
votes
2answers
933 views

Area Between Three Circles of Differing Radii

From the link in wikipedia http://web.gnowledge.org/wiki/index.php/Area_Between_Three_Circles_of_Differing_Radii OPEN QUESTION: What is the equation, in three variables, relating the radii of ...
6
votes
3answers
2k views

Definite integral: $\displaystyle\int^{4}_0 (16-x^2)^{\frac{3}{2}} dx$

The following integral can be computed using the substitution $x = 4\sin\theta~$ and then proceeding with $dx = 4\cos\theta~ d\theta~$, and evaluating the integral of $\cos^4\theta~$: ...
0
votes
3answers
471 views

Formula for gallons in a trough

I have a trough which is a circular container. How do I determine how many gallons of water it takes to fill up the trough? I was thinking that we measure the height and the width but I think it's a ...
5
votes
1answer
245 views

What is the mathematical principle that describes a series of dots on concentric circles that form a spiral pattern?

Apologies for the vagueness of the question, I'll clean it up once an answer helps me describe it better. I'm fascinated by the pattern demonstrated in this image. It's made up of dots on a series ...
6
votes
4answers
3k views

Can a circle truly exist?

Is a circle more impossible than any other geometrical shape? Is a circle is just an infinitely-sided equilateral parallelogram? Wikipedia says... A circle is a simple shape of Euclidean geometry ...
5
votes
3answers
91 views

Algorithm to determine if a collection of unit discs covers the unit disc centered at the origin?

I have a list of points $ (x_i, y_i) $ for $i = 1...n$. Is there an algorithm to determine if the union of the unit discs centered at these points is a superset of the unit disc centered at $(0, 0)$? ...
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votes
4answers
5k views

How do you find the formula for an area of the circle through integration?

I got this question on my Maths exam today, and the Department of Education has stated it is on the syllabus, but none of the three textbooks I could get my hands mention anything about it. One ...
1
vote
3answers
665 views

Inscribed kissing circles in an isosceles trapezoid

5 equal circles in an isosceles trapezoid. Radius of circle is 4. Find black colored area. I don't have any ideas, could you give me a hand? Thanks.
12
votes
1answer
223 views

A question on circles

Given that a lamp-post can light a surrounding circle of radius 100 m, what is the minimum number of such lamp-posts required to light a circular ground of radius 1000 m.
4
votes
2answers
337 views

Geometry Question: Calculating the length of the side of a triangle inside a circle

Given this picture: The radius of the circle is $30$ inches. The angle between $A$ and $B$ is $22.5$ degrees. How would I calculate the distance (not along the arc, but straight line) from $B$ to ...
2
votes
1answer
630 views

How to check if circles intersect each other?

I'm trying to do trilateration where I know the coordinates of three known points and the estimates of the radii - not guaranteed to be really precise. My question is, how can I check if the circles ...
4
votes
1answer
252 views

How do I find the intersections of 2 circles on earths surface?

I have the circles' center in lat & long, as well as the radius in meters. How do I find the circles intersections? Edit: EXAMPLE: ...
2
votes
1answer
320 views

Generating a random point on the unit circle

I'm trying to figure out a way to generate a random point on the unit circle in an application I am developing (I'm a programmer). So far I have the following (in pseudo-code), where Z is a random ...
2
votes
2answers
2k views

Counting number of distinct regions with intersecting circles

Given $n$ circles of possibly different radii, how many distinct regions can there be? For small $n$, I can work it out with pictures. (I'm pretty sure $n=4$ can yield 13 distinct regions, but not ...
7
votes
3answers
7k views

Finding the intersecting points on two circles

Given 2 circles on a plane, how do you calculate the intersecting points? In this example I can do the calculation using the equilateral triangles that are described by the intersection and centres ...
6
votes
2answers
1k views

How do I calculate the equation of a circle given 3 complex numbers?

Given three complex values (for example, $2i, 4, i+3$), how would you calculate the equation of the circle that contains those three points? I know it has something to do with the cross ratio of the ...
5
votes
3answers
401 views

Find sagitta of a cubic Bézier-described arc

I have a situation where I have an arc that was mangled (irrelevant: by c#'s GraphicsPath.AddArc() function). The original arc is guaranteed to be circular, and the new data I have describes the ...
0
votes
1answer
635 views

Get the relation between X and Y axes in triangle based on the degree between

I have a given degree (0 - 360), and based on it, I'd like to be able to calculate the length of X and Y axis of a triangle built on that angle , if the third side of that triangle is equal to 1. I ...
8
votes
1answer
2k views

How many dimensions does a circle have?

Is a circle just a line (therefore 1 dimension) or is it a 2-dimensional object because it occupies some surface? Thanks in advance!
2
votes
2answers
2k views

Area of a circle externally tangent to three mutually tangent circles

Given 3 equal circles, with 3 points of intersection. The line between two of these intersecting points is 3 feet. They are inside a 4th circle. All circles are tangent to each other. What is the ...
12
votes
2answers
524 views

Covering the plane with disks

How to prove that it is impossible to cover the plane with disks? /The disks are closed disks and two disks can meet (at most) at only one point (obviously on the border)./ Thank you very much in ...
10
votes
5answers
5k views

Calculate the area of the crescent

I found this problem on a thread on Stack overflow where it was posted as "job interview question". Unfortunately I cannot find the question. But I saved the picture and just cannot figure it out. ...
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vote
3answers
7k views

Determine coordinate of intersection between a line and a circle

I'm putting together a simple script in processing to visualise layout possibilities within the fluid environment of a web page. I need some help calculating a point on a circle: The circle is as ...
3
votes
3answers
845 views

Area's of rectangle and circle

If a string with length of 20 cm was to create a rectangle and circle, would area of these objects be the same?
2
votes
2answers
634 views

subvolume area under the intersection of a plane (line) and a cone

I am implementing a conical filter for Gupta-Sproull anti-aliased line algorithm. Given a cone with the total volume of 1 and a radius of 1. Find the subvolume of the intersection of a line. The ...
91
votes
7answers
112k views

How many sides does a circle have?

My son is in 2nd grade. His math teacher gave the class a quiz, and one question was this: If a triangle has 3 sides, and a rectangle has 4 sides, how many sides does a circle have? My first ...
0
votes
1answer
112 views

Finding Two Touching circles with limited information

I am working on a track editor and have found myself in a situation where I need to define two touching circles. Ideally I would like to know the centre point, and radius of these circles. The ...
10
votes
1answer
299 views

Is there a way to represent the interior of a circle with a curve?

As you already know, the interior of a circle is represented by an inequality. For example, $$x^2+y^2\leq1$$ for the unit circle. Today I was thinking by myself and I wondered if there is a curve ...
2
votes
1answer
1k views

Positioning three circles, all of them touching each other

There are three circles, all of them touching each other. The bottom two circles are laying on an imaginary floor, such that they touch the line g=-r as well. Given are all three radii, r1 (A), r2 ...
5
votes
13answers
9k views

how to find center of an arc given start point, end point, radius, and arc direction?

Given an arbitrary arc, where you know the following values: start point (x0,y0), end point (x1,y1), radius (r) and arc direction (e.g. clockwise or counterclockwise from start to end), how can I ...
3
votes
1answer
3k views

rules for circle circumscribing

how can i determine wether a circle can be circumscribed about a quadrilateral?
8
votes
2answers
305 views

If $0$, $z_1$, $z_2$ and $z_3$ are concyclic, then $\frac{1}{z_1}$,$\frac{1}{z_2}$,$\frac{1}{z_3}$ are collinear

If the complex numbers $0$, $z_1$, $z_2$ and $z_3$ are concyclic, prove that $\frac{1}{z_1}$,$\frac{1}{z_2}$,$\frac{1}{z_3}$ are collinear. I really can't seem to get anywhere on this problem, ...
7
votes
2answers
2k views

Inscribed kissing circles in an equilateral triangle

Triangle is equilateral (AB=BC=CA), I need to find AB and R. Any hints? I was trying to make another triangle by connecting centers of small circles but didn't found anything
0
votes
3answers
1k views

Formula to Move the object in Circular Path

I want to move one object (dot) in circular path. By using x and y position of that object. Thanks.
14
votes
1answer
2k views

How many circles to cover 2 times bigger circle?

How many circles (radius – r) are needed to cover circle which radius is 2 times bigger (radius – 2r). I think we need to use area which is $S=\pi R^2$ but I don't really know what to do
5
votes
2answers
657 views

Finding point on a circle

I know how to find a point on a circle given a radius and an angle, but my knowledge of trigonometry doesn't extend much further than that. My question is probably best explained diagrammatically: ...
0
votes
1answer
91 views

What's the name of a part of a circle that's formed by an arbitrary intersecting line?

The curved line is a part of a circle with a center at the lower right corner. What would be the name of the shaded region? Thanks
2
votes
1answer
299 views

Getting a Circular Crown's area and perimeter

Okay, this is really bugging me: My Math book has this practice where I need to get the area and perimeter of the next Circular Crown: $R = 3$cm , $r = 1.75$cm. Well, I do it. But my results ...
5
votes
4answers
1k views

Calculate $\pi$ precisely using integrals?

This is probably a very stupid question, but I just learned about integrals so I was wondering what happens if we calculate the integral of $\sqrt{1 - x^2}$ from $-1$ to $1$. We would get the surface ...
3
votes
1answer
186 views

Maximum gap among N points on a circle

If $N$ points on the circumference of a circle are chosen at random, what is the probability $F(\theta)$ that the maximum gap between neighboring points is at least $\theta$? Because the gaps sum to ...
2
votes
1answer
576 views

the equation of a circle on sphere?

one sphere with radius R,named big sphere,two point on it:a(longitude_a,latitue_a),b(longitude_b,latitude_b), dist(a,b)=r, a as center,r as radius,there is another sphere,named little sphere, now what ...
5
votes
2answers
301 views

name of a shape

Let P be a point, not the center, in the interior of a (round) disk D⊂ℝ² and let A and B be points on ∂D such that the line segments AP and BP have equal length. Choose an arc AB. What's the shape ...
6
votes
2answers
2k views

Prove that three points are enough to draw/define one and only one circle

Prove that three points are enough to draw/define one and only one circle, how would this be done?
2
votes
2answers
3k views

Find Coordinates of Touching Point of a Tangent on a Circle

I have a point 'a' with known coordinates, from which I have drawn a tangent to a circle with centre 'c' which is also known. What is the best way of finding the coordinates of point 'b', the touching ...
6
votes
2answers
332 views

Two points on circle resulting in 5 equal regions

What values of $Z_1$ and $Z_2$ make the five regions of the unit circle, shown below, equal in area? $\overline{Z_1}$ and $\overline{Z_2}$ are conjugates of $Z_1$ and $Z_2$; in other words they lie ...
5
votes
3answers
2k views

How many right angled triangles can a circle have?

Here's what I recall of the question from CNML Grade 11, 2010/2011 Contest #3, Question 7: There are 2010 points on a circle, evenly spaced. Ford Prefect will* randomly choose three points on ...
5
votes
3answers
990 views

How to determine arc measures from angles between secant and tangents (without trigonometry)

Given a circle, a point $H$ outside the circle, segments $\overline{HE}$ and $\overline{HT}$ tangent to the circle at $E$ and $T$, respectively, and points $I$ and $G$ on the circle such that $I$, ...
26
votes
3answers
2k views

Have I made a straight line, or a circle?

(Disclaimer: I'm an engineer) Hi everybody, I found this “riddle” posted on the internet: It's meant as a joke, but I do think it deserves an answer :) A bit of background: the orange and blue ...